NONUNIVERSAL BEHAVIOR OF FINITE QUANTUM HALL SYSTEMS AS A RESULT OF WEAK MACROSCOPIC INHOMOGENEITIES

We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights sigma(xx)(max) compared to t he universal values previously predicted for infinite homogeneous samp les. This effect is expected to occur for the conductivity peaks measu red in standard experimental geometries such as the Hall bar and the C orbino disk. At the lowest temperatures, the decrease in sigma(xx)(max )(T) is found to saturate at values proportional to the difference bet ween the adjacent plateaus in sigma(xy), with a prefactor that depends on the particular realization of disorder in the sample. We argue tha t this provides a possible explanation of the ''nonuniversal scaling'' of sigma(xx)(max) observed in a number of experiments. We also predic t an enhancement of the ''nonlocal'' resistance due to the macroscopic inhomogeneities. We argue that, in the Hall bar with a sharp edge, th e enhanced ''nonlocal'' resistance and the size corrections to the ''l ocal'' resistance R(xx) are directly related. Using this relation, we suggest a method by which the finite-size corrections may be eliminate d from R(xx) and R(xy) in this case.